ABSTRACT

This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects.

chapter 1|18 pages

Curves

chapter 2|12 pages

General Properties of Submanifolds

chapter 3|38 pages

Hypersurfaces

chapter 4|22 pages

Submanifolds in Euclidean Space

chapter 5|20 pages

Submanifolds in Riemannian Space

chapter 6|28 pages

Two-Dimensional Surfaces in £ 4

chapter 7|54 pages

Minimal Submanifolds

chapter 8|60 pages

Grassmann Image of a Submanifold

chapter 9|22 pages

Regular Polyhedra in £ 4 and E N